Chapter 4

Energy, capacity, and fine topology9FF63F7CB15D

Classical energy, capacities, balayage, and fine topology.

Sections and subsections

1. 4.1 Potentials, energy and capacity765E6C8792CB
   1. 4.1.1 Kernel energies and equilibrium measuresFF9D3CA4D463
   2. 4.1.8 Continuous potentials and polar sets12EDE2E332B0
   3. 4.1.13 Relative extremal functions and capacity2B6F9623A939
   4. 4.1.22 Capacitability and exceptional setsE98B97E4C96B
   5. 4.1.28 Dirichlet energy and quasi-continuityEB60B98F8F53
2. 4.2 Fine topology and balayage8618E9B4AA3D
   1. 4.2.1 Fine neighborhoods and thinnessE15D6A501F63
   2. 4.2.9 Green energy and compact reduction27012C9B879C
   3. 4.2.15 Sweeping measures and harmonic measureDB98A10B30F4
   4. 4.2.21 Countable covers and quasi-open setsA51B9EF16CF8
   5. 4.2.24 Complex lines and the choice of topology3AAB9C9B1384
3. 4.3 Polar sets, capacity and sweepingAEB997E884B4
   1. 4.3.1 Global polar functions and exact compact pole sets65321DAEF711
   2. 4.3.3 Boundary minimum principles with polar exceptions5F11D2AF64E9
   3. 4.3.5 Reduction and capacity on an admissible open set0416CDC0A00D
   4. 4.3.8 Sweeping identities and the domination principle1E913881086D
4. 4.4 Perron theory and fine boundary limits5CFAC22DC258
   1. 4.4.1 Perron solutions and completed harmonic measureE00A8C634DA6
   2. 4.4.4 Local barriers, cone regularity and regular exhaustions93318C47A3DE
   3. 4.4.7 Green boundary limits, Kellogg's theorem and planar Greenian setsBD2BAD3CFA50
   4. 4.4.10 Exterior Poisson kernels and Helms's point at infinity43AD76172E0C
   5. 4.4.14 Perron theory on the one-point compactification02718F5DB5E5
   6. 4.4.19 Thinness and fine limits78ACC7C20E8C
   7. 4.4.24 The Wiener criterion and planar continuaED2AAB8DC124
5. 4.5 Green energy and Martin boundaries8D29421CAE4C
   1. 4.5.1 Green energy and the complete positive cone57DD989B07A4
   2. 4.5.7 The Martin boundaryB6BAE13977A4